Rigged character : Curves hairs (converted to a mesh) mades Pose mode laggy
I've partly figured it out.

Please be aware that I'm a beginner, so I would be glad to receive advices from a more advanced user.

1. First : the idea to join the hairs to the body is not necesseraly what I (or you) want.

My hairs are split in 6 parts. Some of them needs physics, other don't, but every parts needs to follow the rig (and so, the body) movements.
More, for performances convenience, it is better to animate the character displaying the less amount of vertices.

Then I parented every hair parts to the rig and the body without joining them :


Select the hair parts, select the rig, Ctrl-P to parent with empty groups.
Select the body (or the object the hairs needs to stick on), select the hairs, go to weight paint mode and transfer weights (Source : by name, applied to All Layers).


Then you hairs will follow the rig &amp; body movements, but you can animate you character while muting the hairs in the outliner.

If you want to add physics to any parented parts (the hairs here), just follow the traditionnal steps.

Secondly, I managed to reduce the number of polygons of my hairs parts.

They currently have less than 100k polygons. It is enough  for me :
Pushing the decimate modifier further, and always use the Clean Up tools after (merge by distance, delete loose, degenerate dissolve) and finally normal recalculation to avoid glitchy behaviors.

I don't like this method as my topology got completely f*cked. I don't encounter issues from that but, if someone read that, please feel free to give me some advices.

PS : Please let me know if my english is not understandable.